A Stochastic Car Following Model

Abstract

Car-following models are an essential part of microscopic traffic simulations. For research regarding traffic safety, traffic simulations need to simulate traffic safety related aspects realistically. That means, for example, accidents and near accidents shall occur in the same quantity and in the same way as in reality. Such simulations can be used to make statements about traffic safety with respect to traffic influencing factors and conditions. However, most car-following models are deterministic and do not incorporate uncertainty and fluctuations of perception and behavior. Also, they are explicitly conflict free. Therefore, they are unsuitable for simulating traffic in the desired way. For that reason, a car following model fulfilling the requirements above was developed.

Inspired by [1], our car-following model is nondeterministic and data-driven. It is based on the data set of the Intelligent Cruise Control Field Operational Test [2], in which instrumented vehicles have been used by 108 voluntary drivers for several weeks yielding trajectories of approximately 88,000 driving kilometres. In our model, the acceleration a of a vehicle depends on the following input: -v, the velocity of the vehicle, -∆v, the difference between the velocity of the preceding vehicle and its own velocity, -g, the gap between the vehicle and the preceding vehicle and -aL, the acceleration of the preceding vehicle. The acceleration a underlies a probability distribution that depends on v, ∆v, g and aL. That means, if v*, ∆v*, g* and aL* are the current values for v, ∆v, g and aL, then there exist a probability distribution F(v*,∆v*,g*,aL*) and the actual acceleration a will be drawn from F(v*,∆v*,g*,aL*). For each tuple (v,∆v,g,aL), the probability distribution F(v,∆v,g,aL) was determined by the data of the FOT. For that, the data of velocity, velocity difference, gap and acceleration of the preceding vehicle were binned, and for each tuple (v,∆v,g,aL) of binned values, the expected acceleration, the variance and the type of distribution were computed and stored in look-up tables. During a simulation, the probability distribution F(v,∆v,g,aL) to a given tuple (v,∆v,g,aL) can be recovered by these look-up tables.

To achieve probability distributions that result in a well behaving car-following model, the data had to be corrected (due to erroneous sensor data) and filtered (due to situations in which the driver reacted to other influences besides the preceding vehicle, e.g. red traffic lights) in numerous steps.

Here, we will present the mentioned correction and filtering steps in detail. Further, we will discuss the derived probability distributions and the calibration of the model. Finally, the model will be evaluated and compared to other existing car-following models in several scenarios with respect to various criteria, e.g. the number of accidents, the distribution of surrogate safety measures, and the fundamental diagram.

Keywords

traffic simulation ; car following models ; traffic safety

References

1. Fancher et al., 1998 Fancher, P., et al. 1998. Intelligent Cruise Control Fiel Operational Test, Final Report. 1998.
2. Helbing and Dirk, 2001 Dirk. Helbing; Traffic and Related Self-Driven Many-Particle Systems; Reviews of Modern Physics, 73 (2001), pp. 1067–1141 2001
3. Helly, 1959 W. Helly; Simulation of bottlenecks in single lane traffic flow; Proceedings of the symposium on theory of traffic flow. 1959 (1959), pp. 207–238
4. Krauß and Stefan, 1998 Krauß, Stefan; Microscopic Modeling of Traffic Flow: Investigation of Collision Free Vehicle Dynamics (PhD thesis); Cologne : University of Cologne (1998), p. 1998
5. Krauß et al., 1997 Krauß, Stefan, Wagner, Peter, Gawron, Christian; Metastable states in a microscopic model of traffic flow; Physical Review E. 1997, 55 (1997), pp. 5597–5602
6. Nagel et al., 2003 K. Nagel, P. Wagner, R. Woesler; Still flowing: approaches to traffic flow and traffic jam modeling; Operations Research. 2003, 51 (2003), pp. 681–710
7. Savitzky and Golay, 1964 A. Savitzky, M.J.E. Golay; Smoothing and Differentiation of Data by Simplified Least Squares Procedures; Anal. Chem., Analytical Chemistry. 1964, 36 (1964), pp. 1627–1639
8. Treiber and Kesting, 2013 Treiber, M. and Kesting, A. 2013. Traffic Flow Dynamics Springer. s.l. : Springer, 2013.
9. Yang and Peng, 2010 H.-H. Yang, H. Peng; Development of an errorable car-following driver model; Vehicle System Dynamics. 2010, 48 (2010), pp. 751–773